Current stock price for XYZ $50.00 Interest rate 3% Dividend rate 0% Option PUT PUT PUT PUT CALL CALL CALL CALL Strike Expiration $30.00 6-months $40.00 6-months $50.00 6-months $50.75 6-months - - - $50.00 6-months $50.75 6-months $55.00 6-months $60.00 6-months Option Price $0.14 $0.77 $2.74 $2.97 $3.48 $2.97 $1.20 $0.15 Implied Vol 40% 32% 22% 21% 22% 21% 19% 15% Delta (AOption/AS) -0.023 -0.123 -0.431 -0.470 0.569 0.530 0.299 0.065 XYZ stock is currently trading at $50 per share. We ask our favourite trading desk to price a bunch of 6-month options on XYZ: 4 puts and 4 calls. The table above gives the information For each option price we've run the price through the Black-Scholes formula and solved for implied volatility. The tables also gives the deltas: the derivative of each option price with respect to the stock price. As you know this means: Leave the implied volatility, the interest rate, and the dividend unchanged Change the current price of the stock by a small amount up and down, say +/- $0.01 Apply the call price or the put price formulas, C(S,t) or P(S,t) and obtain the "stock-price-up" and "stock-price-down" price of the option Numerally compute the derivative AOptions/AS. This is the option's delta at that value of the underlying stock and that implied volatility. It's a measure of how sensitive the option price is to the price of the underlying stock. Note that we could also obtain delta analytically by taking the partial derivative (With respect to S) of the functions C(S,t) and P(S,t). 1. Why is the delta negative for all the puts and positive for all the calls? 2. The $55 strike call is priced at $1.20. Suppose the price of the stock moved up from $50 to $52. For this $55-stike call, what would be its approximate updated price if it got price at the same volatility (19%) as before
Current stock price for XYZ $50.00 Interest rate 3% Dividend rate 0% Option PUT PUT PUT PUT CALL CALL CALL CALL Strike Expiration $30.00 6-months $40.00 6-months $50.00 6-months $50.75 6-months - - - $50.00 6-months $50.75 6-months $55.00 6-months $60.00 6-months Option Price $0.14 $0.77 $2.74 $2.97 $3.48 $2.97 $1.20 $0.15 Implied Vol 40% 32% 22% 21% 22% 21% 19% 15% Delta (AOption/AS) -0.023 -0.123 -0.431 -0.470 0.569 0.530 0.299 0.065 XYZ stock is currently trading at $50 per share. We ask our favourite trading desk to price a bunch of 6-month options on XYZ: 4 puts and 4 calls. The table above gives the information For each option price we've run the price through the Black-Scholes formula and solved for implied volatility. The tables also gives the deltas: the derivative of each option price with respect to the stock price. As you know this means: Leave the implied volatility, the interest rate, and the dividend unchanged Change the current price of the stock by a small amount up and down, say +/- $0.01 Apply the call price or the put price formulas, C(S,t) or P(S,t) and obtain the "stock-price-up" and "stock-price-down" price of the option Numerally compute the derivative AOptions/AS. This is the option's delta at that value of the underlying stock and that implied volatility. It's a measure of how sensitive the option price is to the price of the underlying stock. Note that we could also obtain delta analytically by taking the partial derivative (With respect to S) of the functions C(S,t) and P(S,t). 1. Why is the delta negative for all the puts and positive for all the calls? 2. The $55 strike call is priced at $1.20. Suppose the price of the stock moved up from $50 to $52. For this $55-stike call, what would be its approximate updated price if it got price at the same volatility (19%) as before
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
Please answer the highlighted questions with explanation
Transcribed Image Text:Current stock price for XYZ $50.00
Interestrate
3%
Dividend rate
0%
Option
PUT
PUT
PUT
PUT
CALL
CALL
CALL
CALL
Strike Expiration Option Price
$30.00 6-months
$40.00
6-months
$50.00 6-months
$50.75 6-months
$50.00
6-months
$50.75 6-months
$55.00
6-months
$60.00 6-months
$0.14
$0.77
$2.74
$2.97
$3.48
$2.97
$1.20
$0.15
Implied Vol
40%
32%
22%
21%
22%
21%
19%
15%
Delta
(AOption/AS)
-0.023
-0.123
-0.431
-0.470
0.569
0.530
0.299
0.065
XYZ stock is currently trading at $50 per share. We ask our favourite trading desk to price a bunch of
6-month options on XYZ: 4 puts and 4 calls. The table above gives the information
For each option price we've run the price through the Black-Scholes formula and solved for implied
volatility.
The tables also gives the deltas: the derivative of each option price with respect to the stock price. As
you know this means:
Leave the implied volatility, the interest rate, and the dividend unchanged
Change the current price of the stock by a small amount up and down, say +/- $0.01
Apply the call price or the put price formulas, C(S,t) or P(S,t) and obtain the "stock-price-up"
and "stock-price-down" price of the option
Numerally compute the derivative Options/AS. This is the option's delta at that value of
the underlying stock and that implied volatility. It's a measure of how sensitive the option
price is to the price of the underlying stock. Note that we could also obtain delta analytically
by taking the partial derivative (With respect to S) of the functions C(S,t) and P(S,t).
1. Why is the delta negative for all the puts and positive for all the calls?
2. The $55 strike call is priced at $1.20. Suppose the price of the stock moved up from $50 to
$52. For this $55-stike call, what would be its approximate updated price if it got price at the
same volatility (19%) as before
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